and to be clear, there is a major difference between a blech and a hot plate. (almost) no one would be matir putting directly on a blech, even with an inverted pan. the kula is for a hot plate which people don't cook on and thereby is not derech bishul.
a blech only serves to make the for garuf v'katum which solves shema yechateh bgachalim (and helps for shehiyah, leaving not fully chokes food on from erev shabbos, and for chazarah (of fully cooked food)). however nesina btchila (putting food anew on the fire) has an added issue of mechzi kmivashel. a blech does not help for that.